In his press conference on day three of the Dharamsala Test, Ravindra Jadeja said something that's rare to hear from an international cricketer - an admission that luck had played some part in his team getting on top of the opposition.

Australia had just slumped to 137 all out in their second innings, and India's fast bowlers, Umesh Yadav and Bhuvneshwar Kumar, had played key roles in causing that to happen, combining to take four for 56 in 17 overs.

Someone asked Jadeja what the difference had been between their bowling and that of Australia's quicks on the same surface.

"There wasn't much of a difference," Jadeja said. "Their fast bowlers, like us, were bowling in good areas, but sometimes good deliveries miss the edge of the bat and at times straight deliveries get you the edge. Today with [David] Warner it was a straight ball that got his edge. That was the breakthrough."

India's quicks, Umesh in particular, had bowled brilliantly with the new ball, but there was some substance to Jadeja's statement. Sometimes, it takes a bit of luck to find the edge. Josh Hazlewood and Pat Cummins had bowled splendidly in India's first innings, and had taken four wickets too, but had to bowl 55 backbreaking - and often heartbreaking, given how much they tested India's batsmen - overs between them.

Had Cummins and Hazlewood heard and understood Jadeja's statement - he spoke in Hindi - they might have hugged him and wept in gratitude.

But you need more than luck to keep finding the edges. You need a bit of help from batsmen. Both of Australia's openers gave Umesh that help. Warner jabbed at him with hard hands while not moving his feet. Matt Renshaw, squared up by a short ball, followed it with his hands, away from his body, uncertainly, playing neither an attacking nor defensive stroke.

Those are the kind of mistakes Australia's openers kept making through the series. Warner had a torrid time through the tour, his defence shaky against both seam and spin. In all, he made 193 runs in four Tests at an average of 24.12. Even when he did make runs, he did not look secure at the crease; in the first innings in Dharamsala, for instance, he kept trying to cut Kuldeep Yadav when given neither the length nor the width to play the shot safely and was eventually dismissed playing that shot.

Renshaw, meanwhile, began his first tour of India with scores of 68, 31 and 60, on two of the most challenging pitches he must have encountered in his young career. After that, his scores tailed away, his last five innings bringing him only 73 runs at an average of 14.60.

Before the tour, Australia's selectors and team management may have feared such a turn of events for their young opener - a bright start, followed by India's spinners working him out and working him over. Except it wasn't the spinners who worked Renshaw out; it was the seamers. Renshaw was out to spin in each of his first three innings of the tour, and out to either Umesh or Ishant Sharma in his last five innings.

On all five occasions, he was out either playing indecisively in the corridor, away from his body, or stuck in the crease when he should have been on the front foot.

In both innings in Dharamsala, Umesh peppered him with short balls. In the first innings, he followed a series of short balls with a full one that swung in through the gate as Renshaw played a leaden-footed drive. In the second, the short ball itself proved the wicket-taker.

There was a pattern to these dismissals, a sense that India had worked out a way to induce uncertainty in Renshaw's mind and feet. In that process, he ended up being far less of a force on the two best batting pitches of the series, in Ranchi and Dharamsala, than in the two heavily bowler-friendly pitches in Pune and Bengaluru.

In contrast, when they came across conditions where bowlers would need to work a little harder to take their wickets, India's openers - and top order, in general - ensured they made the bowlers work that little bit harder. M Vijay got himself out in Ranchi, but only after 183 balls of intense focus and tight defensive technique against an Australian attack that never let up in intensity. KL Rahul got himself out in the first innings in Dharamsala, finally succumbing to Cummins' relentlessly fast and accurate short bowling, but only after he had been at the crease for more than 40 overs.

At no point in either Test did either Vijay or Rahul play the kind of hard-hands jab, away from the body, that cost Warner and Renshaw their wickets in the second innings in Dharamsala. Hazlewood and Cummins beat them on numerous occasions, but they kept their hands close to their body and didn't follow the ball as it seamed or swung away from them.

When they edged the ball, they were still usually playing close to their body, with soft hands. Not long before Hazlewood dismissed him in the first innings in Dharamsala, Vijay had edged another one but had ensured the ball fell well short of the keeper. In the same Test, Warner was dropped in the slips in both innings, both times playing away from his body, but continued to play in the same vein regardless.

Moreover, Vijay and Rahul, unlike Renshaw in particular, did not lose their composure when peppered with short balls. They may have been discomfited by Cummins and Hazlewood's bouncers, but if the next ball was full, they generally got on the front foot, playing it with no aftereffects of what had come before.

In all, it took India a combined 94.4 overs to dismiss both Renshaw and Warner in the four Australian innings in Ranchi and Dharamsala. It took Australia a combined 111 overs to dismiss both Vijay and Rahul in India's two first innings in those two Tests - they did not play a second innings in Ranchi - and a further 23.5 overs in India's second innings in Dharamsala to dismiss Vijay but not Rahul.

Getting opening batsmen out early can have all kinds of knock-on effects on the rest of the innings. It exposes the middle order to a newer ball, allows first- and second-change bowlers to begin their spells against newer, less certain batsmen, and increases the possibility of exposing the batting side's lower order to the second new ball.

A big opening partnership, or even one opener staying in the middle for a long time, changes everything. It ensures an easier introduction to the crease for the batsmen to follow, with a healthier-looking scoreboard, against bowlers who have expended more energy, and against more defensive fields. As has been the case right through the season for India, the ripple effect of the top order's crease occupation can be felt far later, with the lower order facing tiring bowlers in situations where they can bat with freedom.

Both teams' No. 3s made more than 400 runs in the season and were among the runs in the last two Tests. In both Ranchi and Dharamsala, Australia fell short of posting truly daunting first-innings totals despite brilliant hundreds from Steven Smith. In both Tests, India gained the first-innings advantage thanks not only to Cheteshwar Pujara, but also to the work of the batsmen around him, particularly the two above him in the batting order.